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8916dab93b Oliv* .. include:: ../defs.hrst
                 
                 .. _CarbonStore:
                 
                 Internal carbon store and exudation
                 '''''''''''''''''''''''''''''''''''
                 
                 Note: the internal carbon store is currently only implemented for fixed
                 plankton elemental ratios (i.e., :varlink:`DARWIN_ALLOW_NQUOTA`,
                 :varlink:`DARWIN_ALLOW_PQUOTA`, :varlink:`DARWIN_ALLOW_FEQUOTA`,
                 :varlink:`DARWIN_ALLOW_SIQUOTA` all undefined).
                 
                 With :varlink:`DARWIN_ALLOW_CSTORE` defined, nutrient availability limits
                 growth directly rather than via the photosynthesis rate.  The maximum
                 photosynthesis rate (and with it carbon uptake) becomes independent of
                 nutritient limitation,
                 
                 .. math::
                 
                    P^{{\mathrm{C}}{\op{m}}}_j = P_{{\mathrm{C}},j}^{\max} f^{{{\text{phy}}}}_j(T) \gamma_{\op{pCO2}}
                 
                 but the growth rate is limited by the availability of each nutrient,
                 
                 .. math::
                 
                    \mu_j = \min(P^{\op{C}}_j, \mu^{\max\op{N}}_j, \mu^{\max\op{P}}_j,
                            \mu^{\max\op{Fe}}_j, \mu^{\max\op{Si}}_j)
                 
                
** Warning **
Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 30.


 Each nutrient’s availability determines a maximum achievable growth rate. Its
                 form depends on whether variable quotas are enabled for the nutrient.
                 For instance for phosphorus, without P quota,
                 
                 .. math::
                    :label: eq_darwin_max_growth_p
                 
                    \mu^{\max\op{P}}_j = \frac{1}{R^{\op{P}:\op{C}}_j} V^{{\mathrm{P}}\max}_j
                            \gamma^{\op{P}}_j f^{\op{up}}_j(T) ( 1 + r^{\op{resp}}_j )
                 
                 and with P quota,
                 
                 .. math::
                    :label: eq_darwin_max_growth_p_noquota
                 
                    \mu^{\max\op{P}}_j = \frac{1}{R^{\op{P}:\op{C}}_j} u^{\mathrm{P}}_j
                            ( 1 + r^{\op{resp}}_j )
                 
                 where :math:`u^{\mathrm{P}}_j` is the carbon-specific uptake rate for phosphorus,
                 
                 .. math::
                 
                    u^{\mathrm{P}}_j = V^{{\mathrm{P}}\max}_j \frac{\mathrm{PO}_4}{\mathrm{PO}_4 + k^{\op{PO4}}_j}
                               {{\text{reg}}}^{Q{\mathrm{P}}}_j \cdot f^{{\text{up}}}_j(T)
                 
                 and the respiration rate is
                 
                 .. math::
                 
                    r^{\op{resp}}_j = r^{\op{resp}\max}_j f^{\op{remin}}(T) \frac{c_j - c_j^{\min}}{c_j}
                 
                 Other elements work analogously, except that the maximum nitrogen uptake rate
                 for the case without nitrogen quotas is more complex,
                 
                 .. math::
                 
                    \mu^{\max\op{N}}_j = \frac{1}{R^{\op{P}:\op{C}}_j} u^{{\mathrm{N}}\max}_j
                            ( 1 + r^{\op{resp}}_j )
                 
                 where
                 
                 .. math::
                 
                    u^{{\mathrm{N}}\max}_j = \max( u^{{\mathrm{NO3}}\max}_j,
                         u^{{\mathrm{NO2}}\max}_j, u^{{\mathrm{NH4}}\max}_j )
                 
                 with
                 
                 .. math::
                 
                    u^{{\mathrm{N..}}\max}_j = V^{{\mathrm{N..}}\max}_j \gamma^{\op{N..}}_j
                             f^{\op{up}}_j(T)
                 
                 Part of the excess carbon is exuded to become DOC,
                 
                 .. math::
                 
                    E^{\op{C}}_j = (P^{\op{C}}_j - \mu_j) f^{\op{exude}}_j c_j
                 
                 and part stored as fat,
                 
                 .. math::
                 
                    U^{\op{fat}}_j = (P^{\op{C}}_j - \mu_j) (1 - f^{\op{exude}}_j) c_j \;.
                 
                 The Chlorophyll synthesis rate is based on the growth rate (as before).
                 
                 .. csv-table:: Exudation parameters
                    :delim: &
                    :widths: 13,20,17,15,15,20
                    :class: longtable
                    :header: Trait, Param, Symbol, Default, Units, Description
                 
                    :varlink:`FracExudeC` & :varlink:`a_FracExudeC` & :math:`f^{\op{exude}}_j` & 0.3 &  & fraction of excess carbon exuded

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